There are two main ways to customize your horse in DR (aside from getting a different horse) - adding armor or barding. Armor is easy to understand, even if we're talking about a horse rather than a person, but barding is probably a new word for a lot of people, so let's get to that first.
And here again there are multiple ways to customize - you can choose the style of barding, the style of trim, and whether or not your reins get prettified. The barding styles:
Trim styles:
Plain |
 |
Solid |
 |
Triangle |
 |
Square |
 |
Scallop |
 |
And finally, reins vs. no reins: